On number of hypersurfaces containing projective curves

Details On number of hypersurfaces containing projective curves On number of hypersurfaces containing projective curves

1995-04-04

arxiv.org/abs/alg-geom/9504002v1

Mathematics

Algebraic Geometry

14 pages, no figures, AMSTeX v 2.1 with amsppt

Scientific paper

Generalizing a classical lemma of Castelnuovo, we characterize rational
normal curves (resp. linearly normal elliptic curves) as curves $C\subset
\PP^n$ such that the number of linearly independent hypersurfaces $Z\supset C$
of given degree~$m$ is maximal (resp. next to maximal).

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